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A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing

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  • Mark Stedman
  • Luca Capriotti

Abstract

We generalize a semi-classical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach makes it a viable alternative to fully-numerical schemes for a variety of applications in derivatives pricing.

Suggested Citation

  • Mark Stedman & Luca Capriotti, 2024. "A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing," Papers 2408.02064, arXiv.org.
    • Handle: RePEc:arx:papers:2408.02064
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